Please correct me if I'm wrong. I checked the gov.uk website to find the right visa & they have suggested that I could apply for family visa which would help them to stay in the UK for 2.5 years.
This is the adult dependent relative visa. It is the most difficult visa to get and if you take the risk to apply and they are refused (highly likely), it shuts the door to any future visitor visas for them. The links below explain the requirements and difficulty in getting such a visa.
The UK does not support chain migration of family members. The rules were made a lot tougher in July 2012 in terms of bringing parents to the UK. The approval rate of the adult dependent visa is VERY low and often only successful after very lengthy and expensive court process and usually where the costs of care in the home country are exceptionally high. As your parents are from India, the risk of refusal is extremely high as the cost of care is cheap there.
https://www.immigrationboards.com/immig ... 87771.html
https://www.immigrationboards.com/immig ... 42420.html
You could apply for a longer term visitor visa, but they still cannot stay in the UK for longer than 6 months and also cannot be making the UK their home by spending more time in the UK than they do in India. If the IO on arrival in the UK suspects this, their visitor visas can be cancelled and they will be returned to India and future visitor visas will also be difficult to get.